A) -2
B) 2
C) -3
D) 4
Correct Answer: B
Solution :
Let 3 distinct numbers are a, ar, \[a{{r}^{2}}\] given \[a+b+c=xb\] \[a+ar+a{{r}^{2}}=xar\] \[1+r+{{r}^{2}}=xr\] \[{{r}^{2}}+r\left( 1-x \right)+1=0\] \[D\,\,>\,\,0\] \[{{(1-x)}^{2}}-4\,\,\ge \,\,0\] \[(1-x)-2)(1-x+2)\,\,\ge \,\,0\] \[\left( x\text{ }+\text{ }1 \right)\text{ }\left( x\text{ }-\text{ }3 \right)\text{ }\ge \text{ }0\] \[x\le \,-1\,\,\,\,or\,\,\,\,x\,\,\ge \,\,3\]
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